Question
Asked Oct 14, 2019

A chemist has two alloys, one of which is 5% gold and 10% lead and the other which is 20% gold and 50% lead. How many grams of each of the two alloys should be used to make an alloy that contains 39 g of gold and 87 g of lead?

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Expert Answer

Step 1

Given,

          A chemist has two alloys, one of which is 5% gold and 10% lead and the other which is 20% gold and 50% lead. 

The each of the two alloys should be used to make an alloy that contains 39 g of gold and 87 g of lead.

Let amount of 1st alloy be x and amount of 2nd alloy be y.

Since, amount of gold is 39 grams.
.5% of x 20% of y
39
0.05x0.2y = 39
(i)
And amount of lead is 87 grams
10% of x50% of y 87
0.1x 0.5y 87
(ii)
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Since, amount of gold is 39 grams. .5% of x 20% of y 39 0.05x0.2y = 39 (i) And amount of lead is 87 grams 10% of x50% of y 87 0.1x 0.5y 87 (ii)

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Step 2

Now,

...
2(i) (ii2 (0.05x 0.2y) (0.1x 0.5y) 2(39) - 87
— 0.1х + 0.4y — 0.1х — 0.5у %3D 78 — 87
0.1y 9
y 90
So, from equation (ii), we have
0.1x 0.5(90) = 87
0.1x 45 87
0.1x 42
x = 420
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2(i) (ii2 (0.05x 0.2y) (0.1x 0.5y) 2(39) - 87 — 0.1х + 0.4y — 0.1х — 0.5у %3D 78 — 87 0.1y 9 y 90 So, from equation (ii), we have 0.1x 0.5(90) = 87 0.1x 45 87 0.1x 42 x = 420

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